There are some researchers who claim to be able to grow CTCs, but the problem is that there is more than one type of CTC.
You have epithelial-, mesenchymal-, endothelial-, stromal- and stem cells, macrophages and giant multiploid cells that fall under the definition of "CTC".
Yes, this is possible in xenograft models injected with cancer cell lines capable of clonogenic expansion. Typically, one would plate the freshly harvested blood after lysing red blood cells (which would otherwise be toxic) and select for a marker (e.g. puromycin) expressed by the cancer cells. After 3 weeks to a month, large colonies of cancer cells would be present on the plate.
I do not have enough experience with expanding CTCs from human blood to be able to comment on it.
It is possible, although quite challenging. The concerns about doing this is whether your cultured cells have the same phenotype as the isolated ones, since the culture conditions might select for different clones.
This article ight be usefull for you:
Science. 2014 Jul 11; 345(6193): 216–220.
doi: 10.1126/science.1253533
Ex vivo culture of circulating breast tumor cells for individualized testing of drug susceptibility
Min Yu,1,2,* Aditya Bardia,1,3 Nicola Aceto,1 Francesca Bersani,1 Marissa W. Madden,1 Maria C. Donaldson,1 Rushil Desai,1 Huili Zhu,1 Valentine Comaills,1 Zongli Zheng,1,4,5 Ben S. Wittner,1 Petar Stojanov,6 Elena Brachtel,4 Dennis Sgroi,1,4 Ravi Kapur,7 Toshihiro Shioda,1,3 David T. Ting,1,3 Sridhar Ramaswamy,1,3 Gad Getz,1,4,6 A. John Iafrate,1,4 Cyril Benes,1,3 Mehmet Toner,7,8 Shyamala Maheswaran,1,8,† and Daniel A. Haber1,2,3,†